Tuning Fork The end of a tuning fork moves in simple harmonic motion described by the equation . If a tuning fork for the note above middle on an even-tempered scale ( , the tone by which an orchestra tunes itself) has a frequency of 440 hertz (cycles per second), find . If the maximum displacement of the end of the tuning fork is millimeter, determine the equation that describes the movement of the tuning fork.
Source: David Lapp. Physics of Music and Musical Instruments. Medford, M A:Tufts University, 2003
. If the maximum displacement of the end of the tuning fork is millimeter,determine the equation that describes the movement of the tuning fork.
Answer to Problem 53AYU
Explanation of Solution
Given:
The end of a tuning fork moves in simple harmonic motion described by the equation
If a tuning fork for the note above middle on an even–tempered scale (, the tone by which an orchestra 4tunes itself) has a frequency of 440 hertz (cycles per second).find . If the maximum displacement of the end of the tuning fork is millimeter,
Formula used:
Calculation:
The maximum displacement is the amplitude. Therefore .
The frequency is given by
Therefore and the movement of the tuning fork is described by the equation
substituting the values we get,
Chapter 8 Solutions
Precalculus
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